吉林大学学报(地球科学版) ›› 2017, Vol. 47 ›› Issue (5): 1533-1542.doi: 10.13278/j.cnki.jjuese.201705301
张冲1, 黄大年1, 秦朋波2, 吴国超3, 方刚4
Zhang Chong1, Huang Danian1, Qin Pengbo2, Wu Guochao3, Fang Gang4
摘要: 重力场向上延拓是稳定且收敛的过程,而向下延拓是不稳定且发散的过程。为此,本文提出一种重力场向下延拓新方法。首先,对重力场及其垂向一阶导数向上延拓,得到不同高度的重力场垂向导数;然后,基于求解微分方程的三阶Adams-Bashforth多步法,推导出稳定的向下延拓公式;最后,为验证本文方法,将其分别应用于模型数据和实际数据。理论模型试验及误差曲线表明,相对于经典下延方法——傅里叶变换下延法和积分迭代下延法,新方法三阶Adams-Bashforth公式法下延过程稳定,边界效应不明显,下延深度可达5倍点距,下延结果与真实值的相对误差更小,结果更准确。将本文方法应用于加拿大某区实测航空重力数据,得到有效且准确的下延结果,能够识别和圈定一些细小异常特征。
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[1] 高玉文,骆遥,文武.补偿向下延拓方法研究及应用[J].地球物理学报,2012,55(8):2747-2756. Gao Yuwen, Luo Yao, Wen Wu. The Compensation Method for Downward Continuation of Potential Field from Horizontal Plane and Its Application[J]. Chinese Journal of Geophysics, 2012, 55(8):2747-2756. [2] 张辉, 陈龙伟, 任治新,等. 位场向下延拓迭代法收敛性分析及稳健向下延拓方法研究[J]. 地球物理学报, 2009, 52(4):1107-1113. Zhang Hui, Chen Longwei, Ren Zhixin, et al. Analysis on Convergence of Iteration Method for Potential Fields Downward Continuation and Research on Robust Downward Continuation Method[J]. Chinese Journal of Geophysics, 2009, 52(2):511-518. [3] 张志厚, 吴乐园. 位场向下延拓的相关系数法[J]. 吉林大学学报(地球科学版), 2012, 42(6):1912-1919. Zhang Zhihou, Wu Leyuan. Correlation Coefficient Method for Downward Continuation of Potential Fields[J]. Journal of Jilin University (Earth Science Edition), 2012, 42(6):1912-1919. [4] Peters L J. The Direct Approach to Magnetic Inter-pretation and Its Practical Application[J]. Geophysics, 1949, 14(3):290. [5] Dean W C. Frequency Analysis for Gravity and Mag-netic Interpretation[J]. Geophysics, 2002, 23(1):97. [6] 徐世浙. 位场延拓的积分-迭代法[J]. 地球物理学报, 2006, 49(4):1176-1182. Xu Shizhe. The Integral-Iteration Method for Continuation of Potential Fields[J]. Chinese Journal of Geophysics, 2006, 49(4):1054-1060. [7] 于德武, 龚胜平. 对迭代法位场向下延拓方法的剖析[J]. 吉林大学学报(地球科学版), 2015, 45(3):934-940. Yu Dewu, Gong Shengping. Analysis of the Potential Field Downward Continuation Iteration Method[J]. Journal of Jilin University (Earth Science Edition), 2015, 45(3):934-940. [8] Tikhonov A N,Glasko V B,Litvinenko O K,et al. Analytic Continuation of a Potential in the Direction of Disturbing Masses by the Regularization Method[J]. Izv Earth Physics, 1968, 12:30-48. [9] Clarke G K C. Optimum Second-Derivative and Down-ward-Continuation Filters[J]. Geophysics, 2012, 34(3), 424. [10] Pawlowski R S. Preferential Continuation for Poten-tial-Field Anomaly Enhancement[J]. Geophysics, 1995, 60(2):390-398. [11] 王彦国, 王祝文, 张凤旭,等. 位场向下延拓的导数迭代法[J]. 吉林大学学报(地球科学版), 2012, 42(1):240-245. Wang Yanguo, Wang Zhuwen, Zhang Fengxu, et al. Derivative-Iteration Method for Downward Continuation of Potential Fields[J]. Journal of Jilin University (Earth Science Edition), 2012, 42(1):240-245. [12] 陈生昌, 肖鹏飞. 位场向下延拓的波数域广义逆算法[J]. 地球物理学报, 2007, 50(6):1816-1822. Chen Shengchang, Xiao Pengfei. Wavenumber Domain Generalized Inverse Algorithm for Potential Field Downward Continuation[J]. Chinese Journal of Geophysics, 2007, 50(6):1571-1579. [13] Blakely R J. Potential Theory in Gravity and Mag-netic Applications[M]. Cambridge:Cambridge University Press, 2003. [14] 曾华霖. 重力场与重力勘探[M]. 北京:地质出版社, 2005. Zeng Hualin. Gravity Field and Gravity Exploration[M]. Beijing:Geological Publishing House, 2005. [15] Fedi M, Florio G. A Stable Downward Continuation by Using the ISVD Method[J]. Geophysical Journal International, 2002, 151(1):146-156. [16] Fornberg B. Calculation of Weights in Finite Diffe-rence Formulas[J]. Siam Review, 2002, 40(3):685-691. [17] 刘冬兵. 四阶Adams-Bashforth组合公式的预估-校正方法的对比试验[J]. 西昌学院学报(自然科学版), 2012, 26(3):43-46. Liu Dongbing. The Comparative Test of Fourth Order Adams-Bashforth Combination Formula Predictor-Corrector Methods[J]. Journal of Xichang College (Natural Science Edition), 2012, 26(3):43-46. [18] 王新民,朱洪亮.工程数据:计算方法[M]. 北京:高等教育出版社, 2005. Wang Xinmin,Zhu Hongliang. Engineering Mathematics:Numerical Methods[M]. Beijing:Higher Education Press, 2005. [19] Butcher J C. Numerical Methods for Ordinary Diffe-rential Equations[M]. Hoboken:Wiley, 2008. [20] 刘东甲, 洪天求, 贾志海,等. 位场向下延拓的波数域迭代法及其收敛性[J]. 地球物理学报, 2009, 52(6):1599-1605. Liu Dongjia, Hong Tianqiu, Jia Zhihai, et al. Wave Number Domain Iteration Method for Downward Continuation of Potential Fields and Its Convergence[J]. Chinese Journal of Geophysics, 2009, 52(6):1599-1605. [21] 于波, 翟国君, 刘雁春,等. 噪声对磁场向下延拓迭代法的计算误差影响分析[J]. 地球物理学报, 2009, 52(8):2182-2188. Yu Bo, Zhai Guojun, Liu Yanchun, et al. Analysis of Noise Effect on the Calculation Error of Downward Continuation with Iteration Method[J]. Chinese Journal of Geophysics, 2009, 52(8):2182-2188. [22] 姚长利, 李宏伟, 郑元满,等. 重磁位场转换计算中迭代法的综合分析与研究[J]. 地球物理学报, 2012, 55(6):2062-2078. Yao Changli, Li Hongwei, Zheng Yuanman, et al. Research on Iteration Method Using in Potential Field Transformations[J]. Chinese Journal of Geophysics, 2012, 55(6):2062-2078. |
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